Explanation Given: Microphones are placed at points ( − c , 0 ) and ( c , 0 ) and the sound is detected at the closer microphone t seconds before being detected at the farther microphone. The speed of sound is 330 meters per second . Formula used: Distance formula: The distance D between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given as shown below. D = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 Calculation: It is given that the sound is detected at the closer microphone t seconds before being detected at the farther microphone. Use the formula t = d v and the distance formula to set up an equation that shows the difference in the times that sound takes to reach each microphone. The equation is given below. ( x − ( − c ) ) 2 + ( y − 0 ) 2 330 − ( x − c ) 2 + ( y − 0 ) 2 330 = t Multiply by 330 on both side of the above equation to simplify the equation. ( x + c ) 2 + ( y − 0 ) 2 − ( x − c ) 2 + ( y − 0 ) 2 = 330 t ( x + c ) 2 + y 2 − ( x − c ) 2 + y 2 = 330 t ( ( x + c ) 2 + y 2 ) 2 = ( 330 t + ( x − c ) 2 + y 2 ) 2 ( x + c ) 2 + y 2 = 330 2 t 2 + ( x − c ) 2 + y 2 + 2 ⋅ 330 t ⋅ ( x − c ) 2 + y 2 Further solve the above equation

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Chapter 8.2, Problem 98E

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To show: The point p(x,y) must be on the hyperbola x23302t2−y24c2−3302t2=14.

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Chapter 8.2, Problem 97E

Chapter 8.2, Problem 99E

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Chapter 8 Solutions

EBK GRAPHICAL APPROACH TO ALGEBRA & TRI

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The point p ( x , y ) must be on the hyperbola x 2 330 2 t 2 − y 2 4 c 2 − 330 2 t 2 = 1 4 .

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To show: The point p(x,y) must be on the hyperbola x23302t2−y24c2−3302t2=14.

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Chapter 8 Solutions